Theme Essential Question: How can you use formulas and geometry to solve real-world and mathematical problems?
Essential Questions: How can geometrically draw shapes, help determine that a given set conditions will produce a specific shape?
Standards:
7.G.2 Draw (with technology) geometricshapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine unique triangle, more than one triangle, or no triangle.
Objectives:
The student will draw triangles given certain sets of conditions, such as
The measures of two angles and the included side (ASA),
The measures of two angles and the non-included side, associated with one of the specific angle (AAS),
The measures of two sides and the included angle (SAS),
The measures of all three sides (SSS),
The measures of all three angles (AAA),
The measure of two sides and the non-included angle, associated with one of the specific sides (SSA)
To determine is a unique triangle, more than one triangle, or no triangle will always be produced.
Recommended:
The student will conclude that for a triangle to result the sum of any two side lengths must be greater than the third side length (this concept is needed in the 8th grade geometry unit).
The student will conclude that the sum of the three angles must equal 180 degrees.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
This lesson is an extention of lesson 4-1.
Assessment: Product
The students will continue with their projects from lesson 4-1 by apply an technology component.
Key Questions
What are the properties of a triangle?
What is a “unique” triangle?
How do you know a triangle is “unique”?
Do three given lengths always create a triangle?
If three given sides make a triangle, is the triangle always unique?
Observable Student Behaviors
The student can determine when a given set of conditions will produce a unique triangle, no triangle, or infinite set of triangles.
Extension:
The students can provide a viable argument to justify when three given sides will produce a triangle.
The student can provide a viable argument to justify the angle sum theorem, s = (n-2)180
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Suggested Activities: Continue with the work from lesson 4-1
Apply their work from lesson 4-1 using technology such as Sketchpad, Geogebra, TI 84 Capri Jr, or other appropriate geometric drawing technolgy
ABC Mastering the Common Core in Mathematics
Types of Angles, Chapter 10.1, p. 116
Types of triangles, Chapter 11.1, p. 124
Types of Quadrilaterals, Chapter 11.2, p. 125
Quadrilaterals and their Properties, Chapter 11.3, p. 126
Types of Polygons, Chapter 11.4, Chapter 11.4, p. 127
Drawing Shapes, Chapter 11.5, p. 128-134
Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 4-2, p. 93-96
Gizmo Correlation: None Available at this time
Teaching the Common Core Math Standards with Hands-On Activities,
7.G.2 – Activity p.80
Highly Recommended None Available at this time
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 10. 4b, p. 432-4
Mathematics in Children's Literature:Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Classifying triangles by sides and angles, finding missing angle measures.
7.G.2 Triangle Inequalities
Students will observe which side lengths make a triangle and investigate the theorem stating that the largest angle is opposite the longest side of a triangle.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Grade: 7 Unit: 4 Week: 2Content: Geometric Drawing (Technology)
Dates: 1/28 – 2/1
Theme Essential Question:
How can you use formulas and geometry to solve real-world and mathematical problems?
Essential Questions:
How can geometrically draw shapes, help determine that a given set conditions will produce a specific shape?
Standards:
Objectives:
- The student will draw triangles given certain sets of conditions, such as
- The measures of two angles and the included side (ASA),
- The measures of two angles and the non-included side, associated with one of the specific angle (AAS),
- The measures of two sides and the included angle (SAS),
- The measures of all three sides (SSS),
- The measures of all three angles (AAA),
- The measure of two sides and the non-included angle, associated with one of the specific sides (SSA)
To determine is a unique triangle, more than one triangle, or no triangle will always be produced.Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
This lesson is an extention of lesson 4-1.
Assessment:
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Suggested Activities:
Continue with the work from lesson 4-1
- Apply their work from lesson 4-1 using technology such as Sketchpad, Geogebra, TI 84 Capri Jr, or other appropriate geometric drawing technolgy
- ABC Mastering the Common Core in Mathematics
- Types of Angles, Chapter 10.1, p. 116
- Types of triangles, Chapter 11.1, p. 124
- Types of Quadrilaterals, Chapter 11.2, p. 125
- Quadrilaterals and their Properties, Chapter 11.3, p. 126
- Types of Polygons, Chapter 11.4, Chapter 11.4, p. 127
- Drawing Shapes, Chapter 11.5, p. 128-134
- Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 4-2, p. 93-96
- Gizmo Correlation: None Available at this time
- Teaching the Common Core Math Standards with Hands-On Activities,
- 7.G.2 – Activity p.80
- Highly Recommended None Available at this time
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.- Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 10. 4b, p. 432-4
- Create a puzzle with unit vocabulary words.
http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576Diverse Learners
Homework: (Teachers Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking| Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Geometry and Literature Titles:
http://sci.tamucc.edu/~eyoung/geometry_literature.html- Measurement and children'e Literature/Ratios
http://sci.tamucc.edu/~eyoung/measure_literature.html- Mathematics in Children's Literature:Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annontated Lists of Children's Literature including the math concepts and grade levels.
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, then look under Math and Literature Bibliographies.- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives:
Games
Videos
SMART Board Lessons, Promethean Lessons
- 7.G.2 All About Triangles
Classifying triangles by sides and angles, finding missing angle measures.- 7.G.2 Triangle Inequalities
Students will observe which side lengths make a triangle and investigate the theorem stating that the largest angle is opposite the longest side of a triangle.- Smart Board rational number lessons
http://exchange.smarttech.com/details.html?id=1764f052-3804-448f-9f12-95bc5646a2ea- Rational numbers Smart Board lessons
http://exchange.smarttech.com/details.html?id=050e54ad-0dea-4080-ae54-975d93487209Other Activities, etc.
- Puzzle Maker
- http://www.discoveryeducation.com/free-puzzlemaker/?CFID=1276695&CFTOKEN=75709576
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Activities and tools:
http://www.shodor.org/interactivate/activities/
Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6